Abstract
In this paper, the stability analysis of linear systems with time-varying delays is studied. A novel Lyapunov method is presented, in which positive definiteness of the matrices in common Lyapunov functionals is relaxed by adding what is referred to as a zero-integral functional (ZIF). A general form of auxiliary polynomial-based functionals that contains such ZIF is given. Choosing polynomials of different order as well as exploring double-delay-product (DDP) terms, novel Lyapunov functionals are constructed, which contribute to a set of improved stability conditions expressed in terms of linear matrix inequalities. Finally, numerical examples are provided to corroborate the merits of the proposed method relative to a number of existing methods, and in particular, the effectiveness of the proposed ZIFs and DDP terms in reducing the conservatism of stability conditions.
Disclosure statement
No potential conflict of interest was reported by the author(s).